Generalized Lyapunov exponents and aspects of the theory of deep learning

TL;DR

This paper explores the application of generalized Lyapunov exponents, originating from dynamical systems theory, to various fields including deep learning, highlighting new metric space methods and their potential in understanding complex systems.

Contribution

It introduces and discusses the use of generalized Lyapunov exponents in deep learning and other mathematical areas, expanding their theoretical framework.

Findings

Generalized Lyapunov exponents can be applied to deep learning models.

Metric space methods provide new insights into system stability.

Connections between dynamical systems and deep learning are explored.

Abstract

We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of Lyapunov exponents originally appearing in the theory of dynamical systems and differential equations. These generalizations appear for example in topology, group theory, probability theory, operator theory and deep learning.